论文标题
关于整体运营商范围的特征
On Characteristics of the Range of Integral Operators
论文作者
论文摘要
我们表明，当且仅当每个正函数的图像在适当的拓扑相方面具有较低的半连续代表时，在$ l^p $空间之间的正算子是通过集成对内核函数给出的。这是对一般Banach晶格中内核操作员的新特征的结果，因为那些可以在固定的可计数正向向量集中表示范围的操作员。对于仅主导非平凡内核操作员的运营商来说，类似的结果表明。
We show that a positive operator between $L^p$-spaces is given by integration against a kernel function if and only if the image of each positive function has a lower semi-continuous representative with respect to a suitable topology. This is a consequence of a new characterization of kernel operators on general Banach lattices as those operators whose range can be represented over a fixed countable set of positive vectors. Similar results are shown to hold for operators that merely dominate a non-trivial kernel operator.
